CN107104788B - Terminal and non-repudiation encryption signature method and device thereof - Google Patents

Terminal and non-repudiation encryption signature method and device thereof Download PDF

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CN107104788B
CN107104788B CN201710254227.2A CN201710254227A CN107104788B CN 107104788 B CN107104788 B CN 107104788B CN 201710254227 A CN201710254227 A CN 201710254227A CN 107104788 B CN107104788 B CN 107104788B
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CN107104788A (en
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程朝辉
杜峰
薛芳芳
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Shenzhen Aolian Information Security Technology Co ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/02—Protecting privacy or anonymity, e.g. protecting personally identifiable information [PII]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/0643—Hash functions, e.g. MD5, SHA, HMAC or f9 MAC
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0819—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s)
    • H04L9/0825—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s) using asymmetric-key encryption or public key infrastructure [PKI], e.g. key signature or public key certificates
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H04L9/0866—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving user or device identifiers, e.g. serial number, physical or biometrical information, DNA, hand-signature or measurable physical characteristics
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3066—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3226—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using a predetermined code, e.g. password, passphrase or PIN
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/06—Authentication

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Abstract

The invention discloses a terminal and a non-repudiation encryption signature method and a non-repudiation encryption signature device thereof, wherein the method comprises the following steps: the encryption signing end obtains identification cryptosystem parameters of a key generation center and generates a key pair of a signature public key and a signature private key; encrypting the message M by using the ID _ B of the decryption signature verification end, and performing short signature on the encrypted result data and the message M by using the signature private key to generate encrypted signature result data; and decrypting and verifying the encrypted signature result data by using the identifier password system parameter, the identifier decryption private key D _ B corresponding to the identifier ID _ B and the signature public key through the decryption and verification end, and if the verification is unsuccessful, decrypting and outputting a null value. In the invention, the encrypted signature result data is formed by the short signature, so that the length of the output result of the encrypted signature end is short, the verification is simple, the privacy of the data is ensured, and the authenticity of the data is also ensured.

Description

Terminal and non-repudiation encryption signature method and device thereof
Technical Field
The invention relates to the field of digital signatures, in particular to a terminal and a non-repudiation encryption signature method and device thereof.
Background
In some security applications, data needs to be protected by encryption, and meanwhile, the authenticity of the identity of a data sender needs to be guaranteed. The general method is to encrypt the data after signing the data, or encrypt the data first and then sign the data. However, such a protection method that performs a complete encryption method and signature method separately results in a total length of the output result of the encryption method and the signature method.
There is a need for a cryptographic signature method with short output length and simple verification method.
Disclosure of Invention
The invention mainly aims to provide a terminal with short output length and simple verification method and a non-repudiation encryption signature method and device thereof.
In order to achieve the above object, the present invention provides a non-repudiation encryption signature method, including:
the encryption signing end obtains identification cryptosystem parameters of a key generation center and generates a key pair of a signature public key and a signature private key;
encrypting the message M by using the identifier ID _ B of the decryption signature verification end, and performing short signature on the message M by using the signature private key to generate encrypted signature result data;
and decrypting and verifying the encrypted signature result data by using the identifier password system parameter, the identifier decryption private key D _ B corresponding to the identifier ID _ B and the signature public key through the decryption and verification end, and if the verification is unsuccessful, decrypting and outputting a null value.
Further, the identification code system parameter is<E,e,P1,P2,[s]P1,[s]P2,H,KDF>(ii) a Wherein the content of the first and second substances,
e is an elliptic curve selected by the key generation center;
e is a bilinear pair;
P1and P2Is a point group G1And G2Two points in (1); g1And G2Two point groups with prime number q of the order on the elliptic curve E are formed;
s is a master private key, which is a randomly selected integer between 0 and q;
[s]p1 is s P1Adding;
[s]p2 is s P2Adding;
h is a mapping function which maps a bit string O to [1, q-1 ];
KDF is a standard key derivation function.
Further, the identification decryption private key D _ B of the decryption signature verification end is:
D_B＝[s/(H(1||ID_B)+s)]P2。
further, the step of acquiring the identification cryptosystem parameter of the key generation center and generating the key pair of the public signature key and the private signature key by the encryption signing terminal includes:
the encryption signing terminal obtains the identification cryptosystem parameter of the key generation center<E,e,P1,P2,[s]P1,[s]P2,H,KDF>；
Randomly selecting an integer x between 0 and q, and taking the x as the signature private key;
selection G1And G2Two points F in1And F2Will be<F1,F2,[x]F2>、<F1,F2,[x]F1>、<F1,F2,f＝e(F1，F2)x>As one of the public signature keys.
Further, said F1＝P1Said F2＝P2。
Further, the step of encrypting the message M by using the identifier ID _ B of the decryption and signature verification end, and performing short signature on the message M by using the signature private key to generate encrypted signature result data includes:
calculating the integer h1＝H(1||ID_B)；
Calculating public key Q _ B ═ h of decryption signature verification end1]P1+[s]P1；
Generating a random number r ∈ [1, q-1 ];
calculating X ═ r]Q _ B, converting X data type into bit string C1；
Calculating w ═ grConverting the data type of w into a bit string U, where g ═ e (P)1，[s]P2)；
Preparing a key derivation input XI, wherein the XI comprises C1Splicing with U;
calculating K kdf (xi) of the same length as M;
calculating C2＝M⊕K；
Preparing a Hash input HI, wherein the HI comprises a Hash operation index, M and U splicing;
calculating the integer h ═ h (hi);
calculate S ═ x/(h + x)]F1Converting S data type into bit stringC3；
Will be provided with<C1,C2,C3>And outputting the data as the encrypted signature result data of the message M.
Further, the step of decrypting and verifying the encrypted signature result data by the decryption and signature verifying end by using the identification cryptosystem parameter, the identification decryption private key D _ B corresponding to the identification ID _ B, and the signature public key, and if the verification is unsuccessful, decrypting and outputting a null value includes:
c is verified through the decryption terminal1Is converted into a point X on the elliptic curve E, and X is checked to be belonged to G1Whether the result is true or not;
if not, the verification fails through the direct judgment of the decryption and signature verification end;
the C is verified through the decryption end3Is converted into a point S on the elliptic curve E, it is checked that S belongs to G1Whether the result is true or not;
if not, the verification fails through the direct judgment of the decryption and signature verification end;
if the X belongs to G1And S ∈ G1If both the two are true, calculating w-e (X, D _ B) by the decryption signature verification end; converting the data type of w into a bit string U;
preparing a key derivation input XI through the decryption signing end, wherein the XI includes C1Splicing with U;
calculating and C through the decryption signature verification end2K ═ kdf (xi) of the same length;
calculating M ═ C through the decryption signature verification end2⊕K；
Preparing a key derivation input HI through the decryption and signature verification end, wherein the HI comprises a hash operation index, M and U splicing;
calculating an integer h ═ h (hi) through the decryption signature verification end;
calculating a public key Q _ A ═ h of the encryption signature end through the decryption signature verification end1]F2+[s]F2；
Calculating u-e (S, Q _ A) by the decryption signature verification terminal;
calculating F-e (F) through the decryption signature verification end1，[x]F2)；
And (4) checking whether f is true or not by the decryption signature checking end, if so, passing the verification, otherwise, failing the verification, and decrypting and outputting a null value.
The invention also provides a non-repudiation encryption signature device, which comprises:
the signature key pair generation unit is used for encrypting the identification cryptosystem parameters of the signature end acquisition key generation center and generating a key pair of a signature public key and a signature private key;
the encrypted signature unit is used for encrypting the message M by using the identifier ID _ B of the decryption signature verification end, and carrying out short signature on the message M by using the signature private key to generate encrypted signature result data;
and the decryption signature verification unit is used for decrypting and verifying the encrypted signature result data by using the identification password system parameter, the identification decryption private key D _ B corresponding to the identification ID _ B and the signature public key through the decryption signature verification end, and if the verification is unsuccessful, decrypting and outputting a null value.
Further, the identification code system parameter is<E,e,P1,P2,[s]P1,[s]P2,H,KDF>(ii) a Wherein the content of the first and second substances,
e is an elliptic curve selected by the key generation center;
e is a bilinear pair;
P1and P2Is a point group G1And G2Two points in (1); g1And G2Two point groups with prime number q of the order on the elliptic curve E are formed;
s is a master private key, which is a randomly selected integer between 0 and q;
[s]p1 is s P1Adding;
[s]p2 is s P2Adding;
h is a mapping function which maps a bit string O to [1, q-1 ];
KDF is a standard key derivation function.
Further, the identification decryption private key D _ B of the decryption signature verification end is:
D_B＝[s/(H(1||ID_B)+s)]P2。
further, the signing key pair generating unit includes:
an obtaining module, configured to obtain the identification cryptosystem parameter by the encryption signing side<E,e,P1,P2,[s]P1,[s]P2,H,KDF>；
The first selection module is used for randomly selecting an integer x between 0 and q, and taking the x as the signature private key;
a second selection module for selecting G1And G2Two points F in1And F2Will be<F1,F2,[x]F2>、<F1,F2,[x]F1>、<F1,F2,f＝e(F1，F2)x>As one of the public signature keys.
Further, said F1＝P1Said F2＝P2。
Further, the cryptographic signature unit includes:
a first calculation module for calculating an integer h1＝H(1||ID_B)；
The second encryption calculation module is used for calculating a public key Q _ B ═ h of the decryption signature verification end1]P1+[s]P1；
A selection module for generating a random number r ∈ [1, q-1 ];
a third calculation module for calculating X ═ r]Q _ B, converting X data type into bit string C1；
A fourth calculation module for calculating w-grConverting the data type of w into a bit string U, where g ═ e (P)1，[s]P2)；
An encryption fifth calculation module, preparing a key derivation input XI, XI comprising C1And U, optionally, ID _ B can be spliced;
a sixth encryption calculation module, configured to calculate K ═ kdf (xi) having the same length as M;
an encrypted seventh calculation module for calculating C2＝M⊕K；
An encryption eighth calculation module, configured to prepare a hash input HI, where the HI includes a hash operation index, and concatenation of M and U;
an encryption ninth calculation module for calculating an integer h ═ h (hi);
a tenth calculation module for calculating S ═ x/(h + x)]F1Converting the S data type into a bit string C3；
An output module for transmitting the encrypted signature to the server through the encryption signature end<C1,C2,C3>And outputting the data as the encrypted signature result data of the message M.
Further, the decryption and signature verification unit comprises:
a first selection judgment module for decrypting and verifying the signature end and the terminal C1Is converted into a point X on the elliptic curve E, and X is checked to be belonged to G1Whether the result is true or not;
a first verification module for determining if X belongs to G1If the verification fails, the verification fails through direct judgment of the decryption and signature verification end;
a second selection judgment module for decrypting and verifying the signature end and the terminal C3Is converted into a point S on the elliptic curve E, it is checked that S belongs to G1Whether the result is true or not;
a second verification module for verifying if S ∈ G1If the verification fails, the verification fails through direct judgment of the decryption and signature verification end;
a first calculation module for decrypting if X belongs to G1And S ∈ G1If both the two are true, calculating w-e (X, D _ B) by the decryption signature verification end; converting the data type of w into a bit string U;
a decryption second calculation module for preparing a key derivation input XI through the decryption signature end, wherein the XI includes C1Splicing with U;
a third decryption computation module for computing and computing the sum C through the decryption signature verification end2K ═ kdf (xi) of the same length;
a decryption fourth calculation module for calculating M ═ C through the decryption signature verification end2⊕K；
A decryption fifth calculation module, configured to prepare a hash input HI through the decryption and signature verification end, where the HI includes a hash operation index, and concatenation of M and U;
a decryption sixth calculating module, configured to calculate, by the decryption signature verification end, an integer h ═ h (hi);
a seventh decryption calculation module, configured to calculate, by the decryption and signature verification end, a public key Q _ a ═ h of the encryption signature end1]F2+[s]F2；
An eighth decryption calculation module, configured to calculate u-e (S, Q _ a) through the decryption signature verification end;
a decryption ninth calculation module, configured to calculate F ═ e (F) through the decryption signature verification end1，[x]F2)；
And the third verification module is used for verifying whether f is satisfied or not through the decryption signature verification end, if so, the verification is passed, and otherwise, the verification fails.
The invention also provides a terminal, which comprises a memory and a processor;
the memory is used for storing a program for supporting the non-repudiation encryption signing device to execute any one of the non-repudiation encryption signing methods;
the processor is configured to execute programs stored in the memory.
According to the terminal and the non-repudiation signature method and device thereof, the encrypted signature result data is formed by the short signature, so that the length of the output result of the encrypted signature end is short, the verification is simple, and the privacy of the data and the authenticity of the data are ensured.
Drawings
FIG. 1 is a flowchart illustrating a non-repudiatable signature method according to an embodiment of the present invention;
FIG. 2 is a flowchart illustrating a method for generating a key pair of a public signature key and a private signature key according to an embodiment of the present invention;
FIG. 3 is a flowchart illustrating a method for generating cryptographic signature result data according to an embodiment of the present invention;
FIG. 4 is a flowchart illustrating a method for decrypting and verifying encrypted signature result data according to an embodiment of the present invention;
FIG. 5 is a block diagram of a non-repudiated signature device according to one embodiment of the present invention;
FIG. 6 is a block diagram illustrating a schematic structure of an obtaining unit according to an embodiment of the present invention;
FIG. 7 is a block diagram illustrating a schematic structure of an obtaining unit according to an embodiment of the present invention;
FIG. 8 is a block diagram illustrating the structure of a decryption and signature verification unit according to an embodiment of the present invention;
fig. 9 is a block diagram illustrating a structure of a terminal according to an embodiment of the present invention.
The implementation, functional features and advantages of the objects of the present invention will be further explained with reference to the accompanying drawings.
Detailed Description
It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, an embodiment of the present invention provides a non-repudiation cryptographic signature method, including:
s1, the encryption signing terminal obtains the identification cryptosystem parameter of the key generation center to generate a key pair of a signature public key and a signature private key;
s2, encrypting the message M by using the ID _ B of the decryption signature verification end, and carrying out short signature on the message M by using the signature private key to generate encrypted signature result data;
s3, decrypting and verifying the encrypted signature result data by the decryption and verification end by using the identification password system parameter, the identification decryption private key D _ B corresponding to the identification ID _ B and the signature public key, and if the verification is unsuccessful, decrypting and outputting a null value.
As described in the step S1, the decryption signature verification end and the encryption signature end are intelligent electronic devices, such as a computer, a notebook computer, a smart phone, a tablet computer, and the like; when the intelligent electronic device is cryptographically signed, i.e.The signature end is an encryption signature end, and the signature is a decryption signature end when the signature is decrypted and verified. The key generation center is a key management center, is an important component of public key infrastructure, provides key services such as key generation, storage, backup, update, recovery, query and the like, and can solve the key management problem brought by large-scale cryptographic technology application in a distributed enterprise application environment. The key generation center generates identification cryptosystem parameters of<E,e,P1,P2,[s]P1,[s]P2,H,KDF>(ii) a Wherein the content of the first and second substances,
e is an elliptic curve selected by the key generation center;
e is a bilinear pair;
P1and P2Is a point group G1And G2Two points in (1); g1And G2Two point groups with prime number q of the order on the elliptic curve E are formed;
s is a master private key, which is a randomly selected integer between 0 and q;
[s]p1 is s P1Adding;
[s]p2 is s P2Adding;
h is a mapping function which maps a bit string O to [1, q-1 ];
KDF is a standard key derivation function.
G ═ e (P) can also be added to the above parameters of the identification cryptosystem1，[s]P2) I.e. identify the parameter of the cryptosystem as<E,e,P1,P2,[s]P1,[s]P2,g＝e(P1，[s]P2,H,KDF>Because g ═ e (P)1，[s]P2) It can be calculated by known parameters, so it can be added or not added to the above-mentioned identification cryptosystem parameters as required.
The public signature key and the private signature key of the encrypted signature end are calculated by using parameters in the identification cryptosystem parameters, but are not required to be generated in a secret key generation center, but are finished at the encrypted signature end, and the message M is not required to be sent to the secret key generation center for encryption processing and the like.
As described in step S2, since the encrypted signature result data is formed by a short signature, the output result length of the encrypted signature side is short.
As described in the above step S3, the decryption and signature verification terminal obtains the specified parameters by using the preset rule to decrypt and verify the encrypted signature result data. In the process of signature verification, the identification decryption private key D _ B is obtained by using the identification ID _ B of the decryption signature verification end and a preset calculation rule, in this embodiment, D _ B is ═ s/(H (1| | | ID _ B) + s)]P2。
Referring to fig. 2, in this embodiment, the step S1, in which the encryption signing side obtains the id cryptosystem parameter of the key generation center, and generates a key pair of the public signature key and the private signature key, includes:
s101, the encryption signing terminal obtains the above identification cryptosystem parameters of the key generation center<E,e,P1,P2,[s]P1,[s]P2,H,KDF>；
S102, randomly selecting an integer x from 0 to q, and taking the x as the signature private key;
s103, selecting G1And G2Two points F in1And F2Will be<F1,F2,[x]F2>、<F1,F2,[x]F1>、<F1,F2,f＝e(F1，F2)x>As one of the public signature keys.
As described in the above steps S101, S102 and S103, the process of generating the private signature key and the public signature key for the cryptographic signature end is described. In this embodiment, F can be selected1＝P1，F2＝P2And later-period calculation, verification and the like are facilitated.
Referring to fig. 3, in this embodiment, the step S2 of encrypting the message M by using the identifier ID _ B of the decryption and signature verification end, and performing short signature on the message M by using the signature private key to generate encrypted signature result data includes:
s201, calculating an integer h1＝H(1||ID_B)；
S202, calculating a public key Q _ B ═ h of a decryption signature verification end1]P1+[s]P1；
S203, generating a random number r belongs to [1, q-1 ];
s204, calculating X ═ r]Q _ B, converting X data type into bit string C1；
S205, calculating w ═ grConverting the data type of w into a bit string U, where g ═ e (P)1，[s]P2)；
S206, preparing a key derivation input XI, wherein the XI comprises C1And U, optionally, ID _ B can be spliced;
s207, calculating K ═ kdf (xi) of the same length as M;
s208, calculating C2＝M⊕K；
S209, preparing a Hash input HI, wherein the HI comprises a Hash operation index, M and U splicing, and optionally C1、ID_A、ID_B；
S210, calculating an integer h ═ h (hi);
s211, calculate S ═ x/(h + x)]F1Converting the S data type into a bit string C3；
S212, mixing<C1,C2,C3>And outputting the data as the encrypted signature result data of the message M.
As described in the above steps S201 to S212, the specific process of performing encryption signature on the message M by using the parameters such as the public signature key and the private signature key is a short signature process, and the length of the message M after encryption signature is small. The operation index is used for distinguishing each hash operation in the calculation process. The value of the hash index is not particularly required, and the hash index used by different hash operations is only required to be different, for example, in H (2M U C1 ID _ a ID _ B), the operation index is 2.
Referring to fig. 4, in this embodiment, the step S3 of decrypting and verifying the encrypted signature result data by using, by the decryption and verification terminal, the identification decryption private key D _ B corresponding to the identification ID _ B and the signature public key, and if the verification is unsuccessful, decrypting and outputting a null value includes:
s301, decrypting the signature verification end to obtain the signature verification end C1Is converted into a point X on the elliptic curve E, and X is checked to be belonged to G1Whether the result is true or not;
s302, if not, directly judging through a decryption signature verification end, then failing in verification, and decrypting to output a null value;
s303, the C is processed by the decryption and signature verification end3Is converted into a point S on the elliptic curve E, it is checked that S belongs to G1Whether the result is true or not;
s304, if not, the verification fails through the direct judgment of the decryption and signature verification end;
s305, if the X belongs to G1And S ∈ G1If both the two are true, calculating w-e (X, D _ B) by the decryption signature verification end; converting the data type of w into a bit string U;
s306, preparing a key derivation input XI through the decryption signature verification terminal, wherein the XI comprises C1And U, optionally, ID _ B can be spliced;
s307, calculating and C through decryption and signature verification end2K ═ kdf (xi) of the same length; s308, calculating that M is equal to C through a decryption signature verification end2⊕K；
S309, preparing a key derivation input HI through the decryption signature verification end, wherein the HI comprises a hash operation index, M and U splicing, and optionally C1、ID_A、ID_B；
S310, calculating an integer h ═ H (HI) through a decryption signature verification end;
s311, calculating a public key Q _ A ═ h of the encrypted signature end through the decrypted signature end1]F2+[s]F2；
S312, calculating u-e (S, Q _ a) by the decryption and signature verification end;
s313, calculating F-e (F) by decrypting the signature verification end1，[x]F2)；
And S314, verifying whether f is satisfied or not by the decryption verification end, if so, verifying to be passed, otherwise, verifying to be failed, and decrypting to output a null value.
As described in the above steps S301 to S314, that is, in the process of decrypting and verifying, the process of decrypting and verifying is simple and safe.
In a specific embodiment, in the whole decryption and signature verification process, three-party cooperation is required, that is, a key generation center, an encryption signature end and a decryption signature verification end, and the process specifically includes:
a bilinear pair is a binary map e with three properties G1xG2→Gt
1. Binary linearity: e ([ s ]]P,[t]Q)＝e(P,Q)st.s,t∈Z/Zq.P∈G1，Q∈G2,G1Is a cyclic group of order q, G2Is a power q group whose subgroup has the order q]P denotes s P additions.
2. Non-degradability: there are non-0-way P and Q, e (P, Q) ≠ 1.
3. Calculability: there is a polynomial time method to calculate e (P, Q).
Bilinear pairings are now known as Weil, Tate, Ate, R-Ate, optimized Ate, and the like on elliptic curves.
Step A: the key generation center selects an elliptic curve E which is characterized by bilinear pairs E capable of being calculated efficiently. Determining two point groups G of prime order q on curve E1And G2. Respectively select G1And G2Two points P in1And P2. Randomly select 0<s<q as the primary private key, calculate s]P1，[s]P2And g ═ e (P)1，[s]P2). Wherein [ s ]]P denotes the standard s P additions. Key generation center public identification cryptosystem parameters<E,e,P1,P2,[s]P1,[s]P2,g＝e(P1，[s]P2),H,KDF>. Wherein g ═ e (P)1，[s]P2) Can be pre-calculated and therefore may not be part of the system parameters; the message mapping function H maps a bit string O to [1, q-1]]The above step (1); the KDF is a standard key derivation function.
B, the key generation center generates an identification decryption private key corresponding to the identification ID _ B:
D_B＝[s/(H(1||ID_BA)+s)]P2and the identification ID _ B is the identification ID _ B of the decryption and signature verification end.
Step C, the encryption signing terminal possesses identification ID _ A, which obtains the secretIdentification cryptosystem parameters that are public by a key generation center<E,e,P1,P2,[s]P1,[s]P2,g＝e(P1，[s]P2),H,KDF>Then, randomly select 0<x<q is an integer x, G is selected1And G2Two points F in1And F2Calculate [ x ]]F2Will be<F1,F2,f＝e(F1，[x]F2)>As its public key data, where F ═ e (F)1，[x]F2) Can be calculated from a two-wire pair, so it can be used without being part of the public key, x as its private signature key. An alternative method is to set F1＝P1，F2＝P2。
Step D, encrypting the public parameters of the system obtained by the signer<E,e,P1,P2,[s]P2,g＝e(P1，[s]P2),H,KDF>And a signature public key<F1,F2>And after signing the private key x, encrypting and signing the message M to a decryption signature checking end. The encryption signature method comprises the following steps:
d1: calculating the integer h1＝H(1||ID_B)；
D2: calculate Q _ B ═ h1]P1+[s]P1；
D3: generating a random number r 1, q-1;
d4: calculating X ═ r]Q _ B, converting X data type into bit string C1；
D5: calculating w ═ grConverting the data type of w into a bit string U;
d6: calculating K ═ KDF (C1| | | U | | | ID _ B) of the same length as M;
d7: calculating C2＝M⊕K；
D8: calculating the integer H ═ H (2| | | M | | | U | | | C1| | | ID _ a | | | ID _ B);
d9: calculate S ═ x/(h + x)]F1Converting the S data type into a bit string C3；
D11: will be provided with<C1,C2,C3>As an output.
Step E, decrypting the public parameters of the system used by the signature verification end<E,e,P1,P2,[s]P2,g＝e(P1，[s]P2),H,KDF>And the identification decryption private key D _ B ═ s/(H (1| | | ID _ B) + s)]P2Public key of signature<F1,F2>For the ciphertext<C1,C2,C3>Decrypting and checking the label, wherein the process is as follows:
e1: c is to be1Is converted into a point X on the elliptic curve E, and X is checked to be belonged to G1If the verification result is not true, the verification is not passed;
e2: subjecting said C to3Is converted into a point S on the elliptic curve E, it is checked that S belongs to G1Whether the result is true or not; if not, directly judging that the verification fails;
e3: calculating w ═ e (X, D _ B); converting the data type of w into a bit string U;
e4: calculating the sum C2K ═ KDF (C1| | U | | | ID _ B) of the same length;
e5: calculating M ═ C2⊕K；
E6: calculate the integer H ═ H (2| | M | | | U | | | C1||ID_A||ID_B)；
E7: calculate Q _ a ═ h1]F2+[s]F2；
E8: calculating u-e (S, Q _ a);
e9: calculating F ═ e (F)1，[x]F2) This step may be stored after pre-calculating f for ID _ a.
E10: checking whether f is true or not, if so, verifying to pass, and outputting M; otherwise, the verification is not passed, and the null value is output through decryption.
According to the non-repudiation signature method provided by the embodiment of the invention, the encrypted signature result data is formed by the short signature, so that the length of the output result of the encrypted signature end is short, the verification is simple, the privacy of the data is ensured, and the authenticity of the data is also ensured.
Referring to fig. 5, an embodiment of the present invention further provides a non-repudiation cryptographic signature apparatus, including:
a signature key pair generating unit 10, configured to encrypt a signature end to obtain an identifier cryptosystem parameter of a key generation center, and generate a key pair of a signature public key and a signature private key;
the encrypted signature unit 20 is configured to encrypt the message M using the identifier ID _ B of the decryption and signature verification end, and perform short signature on the message M using the signature private key to generate encrypted signature result data;
and the decryption signature verification unit 30 is configured to decrypt and verify the signature of the encrypted signature result data by using the identification cryptosystem parameter, the identification decryption private key D _ B corresponding to the identification ID _ B, and the signature public key through the decryption signature verification end, and if the verification is unsuccessful, decrypt and output a null value.
As for the signature key pair generating unit 10, the decryption signature verification end and the encryption signature end are intelligent electronic devices, such as a computer, a notebook computer, a smart phone, a tablet computer, and the like; the intelligent electronic equipment is an encrypted signature end when encrypting the signature, and is a decrypted signature end when decrypting the signature. The key generation center is a key management center, is an important component of public key infrastructure, provides key services such as key generation, storage, backup, update, recovery, query and the like, and can solve the key management problem brought by large-scale cryptographic technology application in a distributed enterprise application environment. The key generation center generates identification cryptosystem parameters of<E,e,P1,P2,[s]P1,[s]P2,H,KDF>(ii) a Wherein the content of the first and second substances,
e is an elliptic curve selected by the key generation center;
e is a bilinear pair;
P1and P2Is a point group G1And G2Two points in (1); g1And G2Two point groups with prime number q of the order on the curve E;
s is a master private key, which is a randomly selected integer between 0 and q;
[s]p1 is s P1Adding;
[s]p2 is s P2Adding;
h is a mapping function which maps a bit string O to [1, q-1 ];
KDF is a standard key derivation function.
In the above-mentioned mark cipherG ═ e (P) can also be added to the code system parameters1，[s]P2) I.e. identify the parameter of the cryptosystem as<E,e,P1,P2,[s]P1,[s]P2,g＝e(P1，[s]P2,H,KDF>Because g ═ e (P)1，[s]P2) It can be calculated by known parameters, so it can be added or not added to the above-mentioned identification cryptosystem parameters as required.
The public signature key and the private signature key of the encrypted signature end are calculated by using parameters in the identification cryptosystem parameters, but are not required to be generated in a secret key generation center, but are finished at the encrypted signature end, and the message M is not required to be sent to the secret key generation center for encryption processing and the like.
Since the encrypted signature result data is formed by a short signature, the encrypted signature end output result length is short in the encrypted signature unit 20.
As mentioned above, the decryption and signature verification unit 30 obtains the specified parameters to decrypt and verify the encrypted signature result data according to the preset rules. In the process of signature verification, the identification decryption private key D _ B is obtained by using the identification ID _ B of the decryption signature verification end and a preset calculation rule, in this embodiment, D _ B is ═ s/(H (1| | | ID _ B) + s)]P2。
Referring to fig. 6, in this embodiment, the signature key pair generation unit 10 includes:
an obtaining module 101, configured to obtain the above-mentioned id cryptosystem parameter of the key generation center at the encryption signing end<E,e,P1,P2,[s]P1,[s]P2,H,KDF>；
A first selection module 102, configured to randomly select an integer x between 0 and q, where x is used as the private signature key;
a second selection module 103 for selecting G1And G2Two points F in1And F2Will be<F1,F2,[x]F2>、<F1,F2,[x]F1>、<F1,F2,f＝e(F1，F2)x>As one ofThe public signature key.
As described above, the obtaining module 101, the first selecting module 102, and the second selecting module 103 are modules that generate a private signature key and a public signature key at the encrypted signature end. In this embodiment, F is1＝P1，F2＝P2And later-period calculation, verification and the like are facilitated.
Referring to fig. 7, in this embodiment, the encryption signing unit 20 includes:
a first calculation module 201 for calculating an integer h1＝H(1||ID_B)；
A second calculating module 202 for calculating a public key Q _ B ═ h of the decrypting and verifying end1]P1+[s]P1；
A selection module 203 for generating a random number r ∈ [1, q-1 ];
a third calculation block 204 for calculating X ═ r]Q _ B, converting X data type into bit string C1；
An encrypted fourth calculation block 205 for calculating w-grConverting the data type of w into a bit string U, where g ═ e (P)1，[s]P2)；
An encryption fifth calculation module 206 prepares a key derivation input XI, XI comprising C1And U, optionally, ID _ B can be spliced;
a sixth encryption calculation module 207, configured to calculate K kdf (xi) having the same length as M;
an encrypted seventh calculation module 208 for calculating C2＝M⊕K；
An eighth encryption calculation module 209, configured to prepare a hash input HI, where the HI includes a hash index, and a concatenation of M and U, and optionally C1、ID_A、ID_B；
An encrypted ninth calculation module 210, configured to calculate an integer h ═ h (hi);
an encryption tenth calculation module 211 for calculating S ═ x/(h + x)]F1Converting the S data type into a bit string C3；
An output module 212 for coupling<C1,C2,C3>And outputting the data as the encrypted signature result data of the message M.
The above is a module for encrypting and short-signing the message M by using the parameters such as the public signature key, the private signature key and the like, and the length of the message M after encryption and signature is smaller. The operation index is used for distinguishing each hash operation in the calculation process. The value of the hash index is not particularly required, and the hash index used by different hash operations is only required to be different, for example, in H (2M U C1 ID _ a ID _ B), the operation index is 2.
Referring to fig. 8, in this embodiment, the decryption and signature verification unit 30 includes:
a first selection judgment module 301, configured to decrypt the signature verification end to obtain C1Is converted into a point X on the elliptic curve E, and X is checked to be belonged to G1Whether the result is true or not;
a first verification module 302 for if X ∈ G1If the verification fails, the verification fails through direct judgment of the decryption and signature verification end, and a null value is output through decryption;
a second selection judgment module 303, configured to verify the signature of C through the decryption module3Is converted into a point S on the elliptic curve E, it is checked that S belongs to G1Whether the result is true or not;
a second verification module 304 for if S e G1If the verification fails, the verification fails through direct judgment of the decryption and signature verification end;
a first calculation module 305 of decryption for if X ∈ G1And S ∈ G1If both the two are true, calculating w-e (X, D _ B) by the decryption signature verification end; converting the data type of w into a bit string U;
a decryption second calculation module 306 for preparing a key derivation input XI via the decryption signature end, wherein the XI includes C1And U, optionally, ID _ B can be spliced;
a third decryption computation module 307 for computing the sum C by decrypting the signature verification end2K ═ kdf (xi) of the same length;
a decryption fourth calculating module 308, configured to calculate M ═ C through the decryption verification end2⊕K；
A fifth decryption calculation module 309, configured to prepare a hash input HI through the decryption and signature verification end, where the HI includes a hash operation index, and concatenation of M and U, and optionally concatenation C1、ID_A、ID_B
A decryption sixth calculating module 310, configured to calculate, by the decryption verification end, an integer h ═ h (hi);
a seventh decryption calculation module 311, configured to calculate a public key Q _ a ═ h of the encrypted signature end through the decryption signature end1]F2+[s]F2；
An eighth decryption calculation module 312, configured to calculate u-e (S, Q _ a) through the decryption verification end;
a ninth decryption calculation module 313 configured to calculate F ═ e (F) through the decryption tag end1，[x]F2)；
And the second verification module 314 is configured to verify whether f ═ u is true through the decryption verification end, if yes, the verification is passed, and otherwise, the verification fails, and the decryption outputs a null value.
The modules are devices used in the process of decrypting and verifying the signature, and the process of decrypting and verifying the signature is simple and safe.
According to the non-repudiation signature device, the encrypted signature result data is formed by the short signature, so that the length of the output result of the encrypted signature end is short, the verification is simple, the privacy of the data is guaranteed, and the authenticity of the data is also guaranteed.
Referring to fig. 9, an embodiment of the present invention further provides a terminal 400, which includes a memory 401 and a processor 402; the memory 401 is used for storing a program for supporting the non-repudiation cryptographic signature device to execute the non-repudiation cryptographic signature method in any one of the above items; the processor 402 is configured to execute programs stored in the memory.
The terminal 400 may be an intelligent electronic device, such as a computer, a notebook computer, a smart phone, a tablet computer, and the like.
The terminal 400 is an encrypted signature end when encrypting a signature, and is a decrypted signature end when decrypting a signature.
In the terminal 400 of the embodiment of the present invention, the encrypted signature result data is formed by the short signature, so that the length of the output result of the encrypted signature end is short, the verification is simple, and the privacy and the authenticity of the data are both ensured.
The above description is only a preferred embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by using the contents of the present specification and the accompanying drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (9)

1. A method of non-repudiation cryptographic signing, comprising:
the encryption signing end obtains identification cryptosystem parameters of a key generation center and generates a key pair of a signature public key and a signature private key; the identification code system parameter is<E,e,P1,P2,[s]P1,[s]P2,H,KDF>(ii) a Wherein E is an elliptic curve selected by the key generation center; e is a bilinear pair; p1And P2Is a point group G1And G2Two points in (1); g1And G2Two point groups with prime number q of the order on the elliptic curve E are formed; s is a master private key, which is a randomly selected integer between 0 and q; [ s ] of]P1 is s P1Adding; [ s ] of]P2 is s P2Adding; h is a mapping function that maps a bit string O to [1, q-1]]The above step (1); KDF is a standard key derivation function;
encrypting the message M by using the identifier ID _ B of the decryption signature verification end, and performing short signature on the message M by using the signature private key to generate encrypted signature result data;
decrypting and verifying the encrypted signature result data by using the identifier password system parameter, the identifier decryption private key D _ B corresponding to the identifier ID _ B and the signature public key through the decryption and verification end, and if the verification is unsuccessful, decrypting and outputting a null value;
the method comprises the following steps that the encryption signing end obtains identification cryptosystem parameters of a key generation center and generates a key pair of a signature public key and a signature private key, and comprises the following steps:
the encryption signing terminal obtains the identification cryptosystem parameter of the key generation center<E,e,P1,P2,[s]P1,[s]P2,H,KDF>；
Randomly selecting an integer x between 0 and q, and taking the x as the signature private key;
selection G1And G2Two points F in1And F2Will be<F1,F2,[x]F2>、<F1,F2,[x]F1>、<F1,F2,f＝e(F1，F2)x>As one of the signature public keys;
the step of encrypting the message M by using the identifier ID _ B of the decryption signature verification end, and performing short signature on the message M by using the signature private key to generate encrypted signature result data comprises the following steps:
calculating the integer H1 ═ H (1| | | ID _ B);
calculating a public key Q _ B ═ h1] P1+ [ s ] P1 of the decryption signature verification end;
generating a random number r ∈ [1, q-1 ];
calculating X ═ r ] Q _ B, converting the X data type to a bit string C1;
calculating w-gr, converting the data type of w into a bit string U, wherein g-e (P1, [ s ] P2);
preparing a key derivation input XI, wherein the XI comprises a concatenation of C1 and U;
calculating K kdf (xi) of the same length as M;
computing
Figure FDA0002381499240000021
Preparing a Hash input HI, wherein the HI comprises a Hash operation index, M and U splicing;
calculating the integer h ═ h (hi);
calculating S ═ x/(h + x) ] F1, and converting the S data type into a bit string C3;
and outputting < C1, C2, C3> as the encrypted signature result data of the message M.
2. The non-repudiation encryption signature method according to claim 1, wherein the identification decryption private key D _ B of the decryption signature verification end is:
D_B＝[s/(H(1||ID_B)+s)]P2。
3. the non-repudiatable cryptographic signature method of claim 1, wherein said F is1＝P1Said F2＝P2。
4. The method for non-repudiation encryption signature according to claim 1 or 3, wherein the step of decrypting and signature verification of the encrypted signature result data by the decryption and signature verification terminal using the identification cryptosystem parameter, the identification decryption private key D _ B corresponding to the identification ID _ B and the signature public key, and if the verification is unsuccessful, decrypting and outputting a null value comprises:
c is verified through the decryption terminal1Is converted into a point X on the elliptic curve E, and X is checked to be belonged to G1Whether the result is true or not; if not, the verification fails through the direct judgment of the decryption and signature verification end;
the C is verified through the decryption end3Is converted into a point S on the elliptic curve E, it is checked that S belongs to G1Whether the result is true or not;
if not, the verification fails through the direct judgment of the decryption and signature verification end;
if the X belongs to G1And S ∈ G1If both the two are true, calculating w-e (X, D _ B) by the decryption signature verification end; converting the data type of w into a bit string U;
preparing a key derivation input XI through the decryption signing end, wherein the XI includes C1Splicing with U;
calculating and C through the decryption signature verification end2K ═ kdf (xi) of the same length;
calculating M ═ C through the decryption signature verification end2⊕K；
Preparing a key derivation input HI through the decryption and signature verification end, wherein the HI comprises a hash operation index, M and U splicing;
calculating an integer h ═ h (hi) through the decryption signature verification end;
calculating a public key Q _ A ═ h of the encryption signature end through the decryption signature verification end1]F2+[s]F2；
Calculating u-e (S, Q _ A) by the decryption signature verification terminal;
calculating F-e (F) through the decryption signature verification end1，[x]F2)；
And (4) checking whether f is true or not by the decryption signature checking end, if so, passing the verification, otherwise, failing the verification, and decrypting and outputting a null value.
5. A non-repudiatable cryptographic signature device, comprising:
the signature key pair generation unit is used for encrypting the identification cryptosystem parameters of the signature end acquisition key generation center and generating a key pair of a signature public key and a signature private key; the identification code system parameter is<E,e,P1,P2,[s]P1,[s]P2,H,KDF>(ii) a Wherein E is an elliptic curve selected by the key generation center; e is a bilinear pair; p1And P2Is a point group G1And G2Two points in (1); g1And G2Two point groups with prime number q of the order on the elliptic curve E are formed; s is a master private key, which is a randomly selected integer between 0 and q; [ s ] of]P1 is s P1Adding; [ s ] of]P2 is s P2Adding; h is a mapping function that maps a bit string O to [1, q-1]]The above step (1); KDF is a standard key derivation function;
the encrypted signature unit is used for encrypting the message M by using the identifier ID _ B of the decryption signature verification end, and carrying out short signature on the message M by using the signature private key to generate encrypted signature result data;
the decryption signature verification unit is used for decrypting and verifying the encrypted signature result data by using the identification cryptosystem parameter, the identification decryption private key D _ B corresponding to the identification ID _ B and the signature public key through the decryption signature verification end, and if the verification is unsuccessful, decrypting and outputting a null value;
wherein the signing key pair generating unit comprises:
an obtaining module, configured to obtain the identification cryptosystem parameter by the encryption signing side<E,e,P1,P2,[s]P1,[s]P2,H,KDF>；
The first selection module is used for randomly selecting an integer x between 0 and q, and taking the x as the signature private key;
a second selection module for selecting G1And G2Two points F in1And F2Will be<F1,F2,[x]F2>、<F1,F2,[x]F1>、<F1,F2,f＝e(F1，F2)x>As one of the signature public keys;
the encryption signature unit comprises:
a first calculation module for calculating an integer h1＝H(1||ID_B)；
The second encryption calculation module is used for calculating a public key Q _ B ═ h of the decryption signature verification end1]P1+[s]P1；
A selection module for generating a random number r ∈ [1, q-1 ];
a third calculation module for calculating X ═ r]Q _ B, converting X data type into bit string C1；
A fourth calculation module for calculating w-grConverting the data type of w into a bit string U, where g ═ e (P)1，[s]P2)；
An encryption fifth calculation module, preparing a key derivation input XI, XI comprising C1Splicing with U;
a sixth encryption calculation module, configured to calculate K ═ kdf (xi) having the same length as M;
an encrypted seventh calculation module for calculating C2＝M⊕K；
An encryption eighth calculation module, configured to prepare a hash input HI, where the HI includes a hash operation index, and concatenation of M and U;
an encryption ninth calculation module for calculating an integer h ═ h (hi);
a tenth calculation module for calculating S ═ x/(h + x)]F1Converting the S data type into a bit string C3；
An output module for transmitting the encrypted signature to the server through the encryption signature end<C1,C2,C3>And outputting the data as the encrypted signature result data of the message M.
6. The non-repudiation encryption signature device as claimed in claim 5, wherein the identification decryption private key D _ B of the decryption signature verification end is:
D_B＝[s/(H(1||ID_B)+s)]P2。
7. the non-repudiatable cryptographic signature device as claimed in claim 5, wherein said F1＝P1Said F2＝P2。
8. The non-repudiatable cryptographic signature device as claimed in claim 5 or 7, wherein said decryption and signature verification unit comprises:
a first selection judgment module for decrypting and verifying the signature end and the terminal C1Is converted into a point X on the elliptic curve E, and X is checked to be belonged to G1Whether the result is true or not;
a first verification module for determining if X belongs to G1If the verification fails, the verification fails through direct judgment of the decryption and signature verification end;
a second selection judgment module for decrypting and verifying the signature end and the terminal C3Is converted into a point S on the elliptic curve E, it is checked that S belongs to G1Whether the result is true or not;
a second verification module for verifying if S ∈ G1If the verification fails, the verification fails through direct judgment of the decryption and signature verification end;
a first calculation module for decrypting if X belongs to G1And S ∈ G1If both are true, calculating w-e (X, D) by the decryption signature verification endB); converting the data type of w into a bit string U;
a decryption second calculation module for preparing a key derivation input XI through the decryption signature end, wherein the XI includes C1Splicing with U;
a third decryption computation module for computing and computing the sum C through the decryption signature verification end2K ═ kdf (xi) of the same length;
a decryption fourth calculation module for calculating M ═ C through the decryption signature verification end2⊕K；
A decryption fifth calculation module, configured to prepare a hash input HI through the decryption and signature verification end, where the HI includes a hash operation index, and concatenation of M and U;
a decryption sixth calculating module, configured to calculate, by the decryption signature verification end, an integer h ═ h (hi);
a seventh decryption calculation module, configured to calculate, by the decryption and signature verification end, a public key Q _ a ═ h of the encryption signature end1]F2+[s]F2；
An eighth decryption calculation module, configured to calculate u-e (S, Q _ a) through the decryption signature verification end;
a decryption ninth calculation module, configured to calculate F ═ e (F) through the decryption signature verification end1，[x]F2)；
And the third verification module is used for verifying whether f is satisfied or not through the decryption signature verification end, if so, the verification is passed, and otherwise, the verification fails.
9. A terminal comprising a memory and a processor;
the memory is used for storing a program for supporting a non-repudiation encryption signing device to execute the non-repudiation encryption signing method of any one of claims 1-4;
the processor is configured to execute programs stored in the memory.
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